A sub-gridding scheme with perfectly matched interface for MRTD method

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A sub-gridding scheme with perfectly matched interface for MRTD method


Author: Choi, Kai-yip
Title: A sub-gridding scheme with perfectly matched interface for MRTD method
Degree: M.Phil.
Year: 2001
Subject: Wavelets (Mathematics)
Hong Kong Polytechnic University -- Dissertations
Department: Dept. of Electronic and Information Engineering
Pages: xvii, 142 leaves : ill. ; 30 cm
Language: English
InnoPac Record: http://library.polyu.edu.hk/record=b1599533
URI: http://theses.lib.polyu.edu.hk/handle/200/4846
Abstract: Recently, the multiresolution time domain method (MRTD) has been applied to many microwave problems. There are two different MRTD schemes. They are MRTD with scaling functions only (S-MRTD) and MRTD with scaling functions and wavelet functions (W-MRTD). In S-MRTD scheme, all the fields are expanded by Battle-Lemarie scaling function with respect to space. In W-MRTD scheme, all the fields are expanded by Battle-Lemarie scaling functions and Battle-Lemarie wavelet functions with respect to space. However, when the W-MRTD is applied to air-filled cavities, spurious mode is found in other published literature. In deriving the updating equations of the W-MRTD, it is necessary to compute several integrals. By modifying one of these integrals, spurious mode of the W-MRTD is removed. Since wavelet is sensitive to sudden change, the W-MRTD will be used when a field problem involves instantaneous strong field variation. Hence, when it is necessary to compute the field accurately within an area, W-MRTD will be used. However, this results in increasing in both computational and memory resources as it is not necessary to have a high level of refinement in all regions. Hence, based on the need of calculating the fields accurately without wasting any unnecessary computer resources, the sub-gridding MRTD is proposed. In sub-gridding MRTD scheme, the whole region is divided into dense grid regions and coarse grid regions. In the dense grid regions, the fields are expanded by both scaling functions and wavelet functions with respect to space. For the coarse grid regions, fields are expanded by scaling functions only. However, non-physical reflection occurs in the boundary between the dense grid region and the coarse grid region. The non-physical reflection is due to the numerical wave of the wavelet coefficients at the boundary, which can be removed by the Anisotropic Perfectly Matched Layer (APML). A sub-gridding MRTD scheme is applied to the two-dimensional problems. The propagation of the electromagnetic wave inside the cavity is considered. The time response are recorded and compared with the results obtained by the S-MRTD and W-MRTD. Also, we have applied the sub-gridding MRTD to study the resonant frequencies of an air-filled cavity. The memory resources and computation time of the sub-gridding MRTD are compared with the traditional FDTD, S-MRTD and the W-MRTD. It is found that the sub-gridding MRTD provides a goad accuracy in measuring the resonant frequencies of the cavity, while it consumes less memory resources and fast computation time, compared with FDTD, S-MRTD and W-MRTD.

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